AP Statistics Chapter 3 TEST

Select the best answer

1

You have data for many families on the parents’ income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot,

the explanatory variable is parents’ income, and you expect to see a positive association.

the explanatory variable is years of education, and you expect to see a negative association.

the explanatory variable is parents’ income, and you expect to see very little association.

the explanatory variable is years of education, and you expect to see a positive association.

the explanatory variable is parents’ income, and you expect to see a negative association.

1

The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by yˆ = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months).

1

Lorena is 22.5 months old. What is her predicted height?

1

Jonathan is 20 months old and is 75 centimeters tall. What is his residual?

1

Which of the following statements is/are true?
I. Correlation and regression require that there are clearly-identified explanatory and response variables.
II. Scatterplots require that both variables be quantitative.
III. Every least-squares regression line passes through

A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). A least squares line was fit to the data. Here is the residual plot from this least-squares fit.

1

What does the residual plot tell you about the linear model?

A residual plot is not an appropriate means for evaluating a linear model.

The residual plot suggests that the model may be linear, but more data points are needed to confirm this.

The residual plot clearly indicates that the data isn’t linear.

The residual plot does not confirm nor rule out the linearity of the data.

The residual plot confirms the linearity of the fuel economy data.

Leonardo da Vinci, the renowned painter, speculated that an ideal human would have an armspan (distance from the outstretched fingertip of the left hand to the outstretched fingertip of the right hand) that was equal to his height. The following computer regression printout shows the results of a least-squares regression of armspan on height, both in inches, for a sample of 18 high school students.

1

Which of the following statements is false?

For every one-inch increase in height, the regression model predicts about a 0.84-inch

increase in armspan.

If one of the students in the sample had a height of 70.5 inches and an armspan of 68

inches, then the residual for this student would be –2.78 inches.

The equation of the LSRL is

The fraction of the variation of armspan length that is accounted for by the least squares regression line of armspan on height is 0.871

The correlation coefficient is 0.871

1

A study found correlation r=0.61 between the sex of a worker and his or her income. From this information, we can conclude that...

an arithmetic mistake was made; this is not a possible value of r

women earn less than men on average

women earn more than men on average

this is nonsense because r makes no sense here

the correlation should have been r= -0.61

1

Which of the following statements about the correlation r are true?
I. The correlation and the slope of the regression line have the same sign
II. A correlation of -0.35 and a correlation of 0.35 show the same degree of association about the regression line
III. A correlation of 0.75 indicates a relationship is 3 times as linear as one for which the correlation is only 0.25

1

A copy machine delader has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations give the data below. What is the y intercept of the least-squares regression line of number of service calls on number of copiers?

Part 2: Free Response

Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

How are traffic delays related to the number of cars on the road? Below is data on the total number of hours of delay per year at 10 major highway intersections in the western United States versus traffic volume (measured by average number of vehicles per day that pass through the intersection).

4

Describe what the scatterplot reveals about the relationship between traffic delays and number of cars on the road.

2

Suppose another data point at (200000, 24000), that is 200,000 vehicles per day and 24,000
hours of delay per year, were added to the plot. What effect, if any, will this new point have
on the correlation between these two variables? Explain.

Below is computer output for the regression of hours of delay versus number of vehicle per day.

2

What is the slope of the regression line? Interpret the slope in the context of this problem.

2

AP Statistics Chapter 3 TEST

You have data for many families on the parents’ income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot,

Lorena is 22.5 months old. What is her predicted height?

Jonathan is 20 months old and is 75 centimeters tall. What is his residual?

Which of the following statements is/are true?
I. Correlation and regression require that there are clearly-identified explanatory and response variables.
II. Scatterplots require that both variables be quantitative.
III. Every least-squares regression line passes through

What does the residual plot tell you about the linear model?

Which of the following statements is false?

A study found correlation r=0.61 between the sex of a worker and his or her income. From this information, we can conclude that...

Describe what the scatterplot reveals about the relationship between traffic delays and number of cars on the road.

Suppose another data point at (200000, 24000), that is 200,000 vehicles per day and 24,000
hours of delay per year, were added to the plot. What effect, if any, will this new point have
on the correlation between these two variables? Explain.

What is the slope of the regression line? Interpret the slope in the context of this problem.

Explain what the quantity S = 3899.57 measures in the context of this problem.

You have data for many families on the parents’ income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot,

Lorena is 22.5 months old. What is her predicted height?

Jonathan is 20 months old and is 75 centimeters tall. What is his residual?

Which of the following statements is/are true?
I. Correlation and regression require that there are clearly-identified explanatory and response variables.
II. Scatterplots require that both variables be quantitative.
III. Every least-squares regression line passes through

What does the residual plot tell you about the linear model?

Which of the following statements is false?

A study found correlation r=0.61 between the sex of a worker and his or her income. From this information, we can conclude that...

Describe what the scatterplot reveals about the relationship between traffic delays and number of cars on the road.

Suppose another data point at (200000, 24000), that is 200,000 vehicles per day and 24,000
hours of delay per year, were added to the plot. What effect, if any, will this new point have
on the correlation between these two variables? Explain.

What is the slope of the regression line? Interpret the slope in the context of this problem.

Explain what the quantity S = 3899.57 measures in the context of this problem.

AP Statistics Chapter 3 TEST

AP Statistics Chapter 3 TEST

You have data for many families on the parents’ income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot,

Lorena is 22.5 months old. What is her predicted height?

Jonathan is 20 months old and is 75 centimeters tall. What is his residual?

Which of the following statements is/are true?I. Correlation and regression require that there are clearly-identified explanatory and response variables.II. Scatterplots require that both variables be quantitative.III. Every least-squares regression line passes through

What does the residual plot tell you about the linear model?

Which of the following statements is false?

A study found correlation r=0.61 between the sex of a worker and his or her income. From this information, we can conclude that...

Describe what the scatterplot reveals about the relationship between traffic delays and number of cars on the road.

Suppose another data point at (200000, 24000), that is 200,000 vehicles per day and 24,000hours of delay per year, were added to the plot. What effect, if any, will this new point haveon the correlation between these two variables? Explain.

What is the slope of the regression line? Interpret the slope in the context of this problem.

Explain what the quantity S = 3899.57 measures in the context of this problem.

You have data for many families on the parents’ income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot,

Lorena is 22.5 months old. What is her predicted height?

Jonathan is 20 months old and is 75 centimeters tall. What is his residual?

Which of the following statements is/are true?I. Correlation and regression require that there are clearly-identified explanatory and response variables.II. Scatterplots require that both variables be quantitative.III. Every least-squares regression line passes through

What does the residual plot tell you about the linear model?

Which of the following statements is false?

A study found correlation r=0.61 between the sex of a worker and his or her income. From this information, we can conclude that...

Describe what the scatterplot reveals about the relationship between traffic delays and number of cars on the road.

Suppose another data point at (200000, 24000), that is 200,000 vehicles per day and 24,000hours of delay per year, were added to the plot. What effect, if any, will this new point haveon the correlation between these two variables? Explain.

What is the slope of the regression line? Interpret the slope in the context of this problem.

Explain what the quantity S = 3899.57 measures in the context of this problem.

Which of the following statements is/are true?
I. Correlation and regression require that there are clearly-identified explanatory and response variables.
II. Scatterplots require that both variables be quantitative.
III. Every least-squares regression line passes through

Suppose another data point at (200000, 24000), that is 200,000 vehicles per day and 24,000
hours of delay per year, were added to the plot. What effect, if any, will this new point have
on the correlation between these two variables? Explain.

Which of the following statements is/are true?
I. Correlation and regression require that there are clearly-identified explanatory and response variables.
II. Scatterplots require that both variables be quantitative.
III. Every least-squares regression line passes through

Suppose another data point at (200000, 24000), that is 200,000 vehicles per day and 24,000
hours of delay per year, were added to the plot. What effect, if any, will this new point have
on the correlation between these two variables? Explain.